6x^5-2x^4+6x^3-12x^5-6x^3-12x^5-6x^4+9x^3=

Solution for 6x^5-2x^4+6x^3-12x^5-6x^3-12x^5-6x^4+9x^3= equation:

Simplifying
6x5 + -2x4 + 6x3 + -12x5 + -6x3 + -12x5 + -6x4 + 9x3 = 0

Reorder the terms:
6x3 + -6x3 + 9x3 + -2x4 + -6x4 + 6x5 + -12x5 + -12x5 = 0

Combine like terms: 6x3 + -6x3 = 0
0 + 9x3 + -2x4 + -6x4 + 6x5 + -12x5 + -12x5 = 0
9x3 + -2x4 + -6x4 + 6x5 + -12x5 + -12x5 = 0

Combine like terms: -2x4 + -6x4 = -8x4
9x3 + -8x4 + 6x5 + -12x5 + -12x5 = 0

Combine like terms: 6x5 + -12x5 = -6x5
9x3 + -8x4 + -6x5 + -12x5 = 0

Combine like terms: -6x5 + -12x5 = -18x5
9x3 + -8x4 + -18x5 = 0

Solving
9x3 + -8x4 + -18x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(9 + -8x + -18x2) = 0

Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(9 + -8x + -18x2)' equal to zero and attempt to solve:

Simplifying
9 + -8x + -18x2 = 0

Solving
9 + -8x + -18x2 = 0

Begin completing the square.  Divide all terms by
-18 the coefficient of the squared term: 

Divide each side by '-18'.
-0.5 + 0.4444444444x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.4444444444x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.4444444444x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.4444444444x + x2 = 0 + 0.5
0.4444444444x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.4444444444x + x2 = 0.5

The x term is 0.4444444444x.  Take half its coefficient (0.2222222222).
Square it (0.04938271604) and add it to both sides.

Add '0.04938271604' to each side of the equation.
0.4444444444x + 0.04938271604 + x2 = 0.5 + 0.04938271604

Reorder the terms:
0.04938271604 + 0.4444444444x + x2 = 0.5 + 0.04938271604

Combine like terms: 0.5 + 0.04938271604 = 0.54938271604
0.04938271604 + 0.4444444444x + x2 = 0.54938271604

Factor a perfect square on the left side:
(x + 0.2222222222)(x + 0.2222222222) = 0.54938271604

Calculate the square root of the right side: 0.741203559

Break this problem into two subproblems by setting 
(x + 0.2222222222) equal to 0.741203559 and -0.741203559.

Subproblem 1
x + 0.2222222222 = 0.741203559

Simplifying
x + 0.2222222222 = 0.741203559

Reorder the terms:
0.2222222222 + x = 0.741203559

Solving
0.2222222222 + x = 0.741203559

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.2222222222' to each side of the equation.
0.2222222222 + -0.2222222222 + x = 0.741203559 + -0.2222222222

Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000
0.0000000000 + x = 0.741203559 + -0.2222222222
x = 0.741203559 + -0.2222222222

Combine like terms: 0.741203559 + -0.2222222222 = 0.5189813368
x = 0.5189813368

Simplifying
x = 0.5189813368

Subproblem 2
x + 0.2222222222 = -0.741203559

Simplifying
x + 0.2222222222 = -0.741203559

Reorder the terms:
0.2222222222 + x = -0.741203559

Solving
0.2222222222 + x = -0.741203559

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.2222222222' to each side of the equation.
0.2222222222 + -0.2222222222 + x = -0.741203559 + -0.2222222222

Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000
0.0000000000 + x = -0.741203559 + -0.2222222222
x = -0.741203559 + -0.2222222222

Combine like terms: -0.741203559 + -0.2222222222 = -0.9634257812
x = -0.9634257812

Simplifying
x = -0.9634257812

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5189813368, -0.9634257812}
Solution
x = {0.5189813368, -0.9634257812}